Chapter 1. On the a-Algebraic Realization Problem -- Chapter 2. Weak Conditional Independence And Relative Invariance in Bayesian Statistics -- Chapter 3. Some Useful Properties of the Dirichlet Process -- Chapter 4. On the Distribution of Jumps of the Dirichlet Process -- Chapter 5. Bayes, Bootstrap, Moments -- Chapter 6. Smooth vs. likelihood estimation for a class of mixtures of discrete distributions -- Chapter 7. Bayesian Encompassing Specification Tests of a Parametric Model against a Non Parametric Alternative -- Chapter 8. Nonparametric Bayesian Survival Analysis -- Chapter 9. Simulation of Posterior Distributions in Nonparametric Censored Analysis -- Chapter 10. Bayesian Identification of Semi-Parametric Binary Response Models -- Chapter 11. Survival Data with Explanatory Processes: A Full Nonparametric Bayesian Analysis -- Chapter 12. Nonparametric Competing Risks Models: Identification and Strong Consistency.

This book is a compilation of unpublished papers written by Jean-Marie Rolin (with several co-authors) on nonparametric bayesian estimation. Jean-Marie was professor of statistics at University of Louvain and died on November 5th, 2018. He made important contributions in mathematical statistics with applications to different fields like econometrics or biometrics.These papers cover a variety of topics, including: • The Mathematical structure of the Bayesian model and the main concepts (sufficiency, ancillarity, invariance…) • Representation of the Dirichlet processes and of the associated Polya urn model and applications to nonparametric bayesian analysis. • Contributions to duration models and to their non parametric bayesian treatment.